Yes, it's not for Tolkien (or us) to decide. We can guess though: if the cosmology of Middle Earth included Hell, he probably went there. Not for certain, though, because there's always the possibility of repentance in freefall, and instant forgiveness. Mortals do not know how Eru operates.

Join us NOW in the Reading Room for detailed discussions of The Hobbit, July 9-Nov. 18!